Your mum's so FAT32...
Not unless industry starts using batteries for storage as well. Currently, the peak power usage has very little to do with residential usage. Where I live, it's always the same as cheap overnight rates on weekends and holidays. Because residential users don't account for that much power. The real power draw comes from industrial and commercial uses.
Doesn't even sound like he was using a lot of stuff. Basically doing laundry and dishes while preparing a big meal. It probably woudn't happen every day, but I could easily see it happening.
I think that power companies should offer more incentives for people to have these in order to smooth out the electricity demand. Imagine if everybody had one. The grid wouldn't need as much capacity, and they would be able to use more renewables because the draw would be constant and people could store their own power. Many electricity companies are already charging higher rates during peak times. This is one way to get rid of the peaks. It's already a $0.05/KWh difference where I live. If the price of these gets low enough, it might make sense for everybody to install one, even without solar panels.
Politics: A strife of interests masquerading as a contest of principles. The conduct of public affairs for private advantage. -- Ambrose Bierce